It is proposed to study the formation of electron donor-acceptor complexes of a series of biologically active barbiturates with a quinoidal enzyme, Coenzyme Q, found in cell respiratory systems. Evidence is given as to the possibility that these complexes contribute to the effects of barbiturate upon cell functions. The objective of this study is to provide a general insight into the physiological state of barbiturate anesthesia through theoretical evidence of drug binding along the respiratory chain in cerebral tissue. Such evidence would open up new roads in the investigation of the primary chemical causes and effects of the hypnotic state. The method involves the use of the Linear Combination of Molecular Orbitals approach which has been applied in the past to series of charge-transfer complexes with consistently good experimental agreement.